As an ex HMIT let me tell you that whilst you don't want to be a "patsy" for HMRC it is,as with most things in life,not a good idea to get on the wrong side of them.All that is likely to do is trigger more unnecessary and unwelcome tax enquiries.
You have been given some sound advice by previous posters on this thread.Please take heed of what they have said (HMRC have a reason for looking at you).

The accounts will have been prepared using the free software available to individuals to enable them to file company accounts and the supporting CT return(this service was available to agents up to three years or so ago - I used to use it).

I use HMRC's system to file nearly all my client's SA returns and have had many issues with FTCR in previous years.There is clearly a software issue as I have previously challenged HMRC on this point - they have simply accepted my figure of FTCR and issued an amended SA302!
I agree with the OP and would simply manually force through the £20 adjustment(not worth a white space comment given the amount involved).

You are correct.The same rules apply to all contractors regardless of tax status.
You must always verify all new subcontractors with HMRC and deduct tax at the rate instructed.Each month you file a return of payments made and tax deducted from those payments and this must be done by 19th of the month if you are to avoid the dreaded penalties!
Any tax deducted from payments made to the company prior to it obtaining gross payment status can be offset against ongoing PAYE liabilities.Your software will/should allow you to enter the monthly sums and this in turn will enable you to file the relevant EPS.

Apologies for the delay in getting back to you.
You are correct in your assertion.
I wasn't sure of the number of years you could claim/get credits for in these circumstances and the 10 year limit was something I seemed to recall from an article I read some considerable time ago prior to the introduction of the new state pension system.My recall is obviously incorrect as the following link suggests you could get credits for up to 22 years!The 20 year limit was again my recall of the limit under the old Home Responsibility Protection rules but I may also be slightly out there!Sorry I cannot be anymore helpful without further research.

It would be better for your client not to work!If your a parent registered for Child Benefit for a child under 12 you get Class 3 credits automatically.However,I think that period may now be limited to 10 years whereas under the old HRP rules it was restricted to 20 years.